VIBRATIONS OF A SPINNING ANNULAR PLATE WITH MULTI-CIRCULAR LINE GUIDES

An analysis of the vibration of a spinning annular plate with grounded circular line guides is presented. The equation of motion for a freely spinning plate is first derived, and traveling modes are introduced so that a modal expansion method can be applied. Galerkin’s method is then employed to yield the discretized equations. The forced vibration due to a circular traveling line load is then obtained in preparation for the employment of receptance. Unlike the ordinary receptance defined in the literature, the traveling line receptance is introduced in this paper. The frequency equation for the spinning plate with grounded circular line guides is obtained, and the effects of guide stiffness and location on the frequency changes are discussed. The mode shapes for one circular line guide are also drawn. The results show that, unlike point supports, a circuit line guide improves the critical rotational speed effectively. Numerical results for two guides are also illustrated. The approach developed can be applied to multi-guide cases without much difficulty. © 1993 Academic Press Limited.